Section Modulus calculation and optimization

Modulus of inertia :

Modulus of Inertia (MOI) is also known as the second moment of area. It is a direct measure of the strength of a component with respect to its area of distribution or cross-section area. More MOI means more resistance toward the deformation of the object. The cross-section may include rectangle, triangle, circle, I section, L section, T section, etc… or any complex CSA. MOI primarily depends on the CSA and the axis about with MOI is considered. For example, a rectangular section with small width and high height has more MOI compared to a rectangular section with more width and small height if we are considering the MOI along the horizontal axis.

Section Modulus :

It is the ratio of MOI and the distance between the neutral axis and the section to be considered. It is a measure of the bending stiffness of the component. Section modulus depends on both area and distance. More the distance from the neutral axis smaller the section modulus, hence the strength of the component is also less.

Section Modulus = MOI / y

Y= distance from the neutral axis to the extreme edge.

Ways to increase the section Modulus:

• Increase the area of the section in the normal direction to the axis of consideration.
• Reduce the total length of the component in the normal direction to the axis of consideration so that the distance between the neutral axis and the extreme point will be reduced as a result the section modulus will be improved.

General data:

Distance between neutral axis and the extreme edge = 440.7 mm

Case 1: Assumed design

Data :

Section Area : 1.356 e+03 mm^2

Y : 440.7 mm

MOI : 2.6621 e+05 mm^4

Note: We only consider the minimum moment of inertia.

Section Modulus = 2.6621 e+05 / 440.7

= 604.06 mm^3

Case 2: The embossing of the inner hood is changed in dimensions

Data :

Section Area : 1.356 e+03 mm^2

Y : 440.7 mm

MOI : 2.4960e+05 mm^4

Section Modulus = 2.4960e+05/ 440.7

= 566.37 mm^3

Case 3: Offsetting the inner hood by 0.5 mm away from the outer hood

Data :

Section Area : 1.356 e+03 mm^2

Y : 440.7 mm

MOI : 2.711 e+05 mm^5

Section Modulus = 2.711 e+05 / 440.7

= 615.15 mm^3

Inference :

• We can clearly see increasing the area of the section increases the section modulus of the component and hence increases the resistance to crush during a frontal crash.
• Case 3 of our study proves to be better than the rest cases that are offsetting 0.5 mm from the outer panel from the previous value gives better results.